Uric acid is more soluble at higher pH values, therefore if you alkalize your body, you reduce the risk of urate kidney stones, and there is a very, very small chance of reducing uric acid elsewhere by a very very small amount. The only reason I produced those charts is because some people recommend baking soda (sodium bicarbonate) as a benefit for gout sufferers, but that is not suitable for high blood pressure sufferers.
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Quite frankly, it is amongst the least useful of information, and certainly nowhere near as important as establishing exactly what your uric acid level is and producing a plan to manage it.
Iron, calories, & purines (in that order) are more important aspects of diet, and if you eat a healthy diet based on fresh food with plenty of fruit & veg, the acid/alkaline charts will probably not be relevant.
I know this doesn't exactly answer your question, but if you could be a bit more specidic about which part you do not understand, I'll try to give a better answer.
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I've never heard of L-Lysing. There is an amino acid called l-lysine, but it has nothing to do with gout.